My research is a part of the combinatoric theory of special functions and has applications in arithmetics and
holomorphic dynamic.
More precisely, my scientific interests are around quasi-symmetrique functions. In order to have a better understanding of their
combinatorics structure, I'm interested in some of their specializations like multiple zeta values, multitangent functions or
the multiple Bernoulli polynomials and numbers. As an example, the particularly rich combinatorics of multiple zeta values
gives us some interesting information on QSym.
The defense of my Ph.D. thesis, entitled "Analytical Invariants of Diffeomorphisms and Multizeta Values" and prepared under the supervising of Jean Ecalle, was the October 19th, 2011, in front of a jury composed with:
The thesis manuscript (in French) is available here:
Here is a condensed version (also in French):
| Database of numerical values of multiple zeta values |
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| Algorithm of numerical computation of holomorphic invariants |
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| Algorithm of numerical computation of multiple zeta values, by R. Crandall |
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| Table of reduction of multitangent functions of weight up to 10 |
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| Tables of multiple Bernoulli numbers and polynomials |
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| Jupyter notebook to draw phase portraits of functions defined and valued in C |
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| O. Bouillot, | Gauss-Laguerre and related quadratures - Explicit formula of the error term, pré-publication |
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| O. Bouillot, | Multiple Bernoulli Polynomials and Numbers, soumis |
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| O. Bouillot, | Mould calculus - On the secondary symmetries, C. R. Acad. Sci. Paris, Ser I, 354, n°10 (2016), p. 965-970. |
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| O. Bouillot, J. Ecalle, | Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas,
120p., 2016, accepté aux actes de la conférence internationnale"Resurgence, Physics and Numbers". |
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| O. Bouillot, | On the Hurwitz Multizeta Functions,, Advances in Applied Mathematics, Volume 71 (2015), p. 68-124. |
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| O. Bouillot, | The Algebra of Hurwitz Multizeta Functions, C. R. Acad. Sci. Paris, Ser I, 352, n°11 (2014), p. 865-869. |
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| O. Bouillot, | The Algebra of Multitangent Functions, Journal of Algebra, 410 (2014), p.148-238. |
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| O. Bouillot | Condensed version of my Ph.D. results 22p., 2012 |
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| O. Bouillot | Analytical Invariants of Diffeomorphisms and Multizeta Values, Ph.D. Thesis, in French Orsay, 2011 |
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| O. Bouillot | Differential proporties of modular forms, Master thesis, 2007, not published. |
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| 29th March 2016 | An example of generalization of Bernoulli numbers and polynomials in higher dimension, Paris XIII seminary (France). |
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| 21th May 2015 | Mould calculus, applied to the generalization of Bernoulli numbers and polynomials to the multiple case, at the conference "Resurgence, Physics and Numbers", Scuola Normale Superiore di Pisa, Centro di Ricerca Matematica Ennio de Georgi, Pise (Italie). |
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| 8th April 2015 | Generalization of Bernoulli numbers and polynomials to the multiple case, UQAM University seminary (Montréal, Canada). | ||
| 30th March 2015 | Computation of analytical invariants of tangent-to-identity diffeomorphism, at the conference "Perspectives on Parabolic Points in Holomorphic Dynamics'', Banff International Research Station, Banff (Canada). | ||
| 25th March 2015 | Computation of analytical invariants of tangent-to-identity diffeomorphisms, Columbus University seminary (USA, Ohio). | ||
| 3th March 2015 | Generalization of Bernoulli numbers and polynomials to the multiple case, Paris XIII seminary (France). | ||
| 17th January 2015 | Algebraic Renormalisation of multizetas and multiple Bernoulli polynomials at the conference Meeting on causal sets, ULCO, Calais (France) | ||
| 17th October 2014 | On the multiple Bernoulli polynomials and numbers, working group C.A.R.M.A., Besse (France). | ||
| 18th August 2014 | Multiple Bernoulli Polynomials, at the conference "Algorithmic and Enumerative Combinatorics Summer School 2014", Hagenberg (Austria). | ||
| 24th March 2014 | Multiple Bernoulli Polynomials, at the conference "72ième Séminaire Lotharingien de Combinatoire", Lyon (France). |
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| 21th January 2014 | About multiple Bernoulli polyomials, seminar in Paris XIII University (France). | ||
| 21th November 2013 | Multiple Bernoulli Polynomials: an Approach from Mould Calculus, at the conference Combinatorial aspects of dynamical systems , C.I.R.M., Marseille (France). | ||
| 1st October 2013 | The algebra of Multitangent Functions, at the conference "New Approaches To Multiple Zeta Values", I.C.M.A.T., Madrid (Spain). | ||
| 13th June 2013 | Two Questions Related to the Bernoulli Numbers and the Multizeta Values, algebraic combinatorics working group of the French G.D.R.I.M., Marne-la-Vallée (France). | ||
| 9th April 2013 | About Hurwitz multizetas function, applications to multitangent functions, at the conference "Combinatorial Hopf Algebras and Mould Calculus", Scuola Normale Superiore di Pisa, Centro di Ricerca Matematica Ennio de Georgi, Pisa (Italia). | ||
| 25th March 2013 | An Embodiment of Quasi-Symmetric Functions: the Hurwitz Multizeta Functions, at the conference "70ième Séminaire Lotharingien de Combinatoire", Ellwangen (Germany). |
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| 1st March 2013 | Multizeta Values: the Approach from the Multitangent Functions, seminar in Hamburg University (Germany). | ||
| 19th Febuary 2013 | The Multitangent Functions, the Point of Vue from Hurwitz Multizeta Functions, seminar in Paris XIII University (France). | ||
| 17th September 2012 | Multitangent Functions, Multizeta Values and Holomorphic Dynamics, at the conference "Renormalization at the confluence of analysis, algebra and geometry", C.I.R.M., Marseille (France). |
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| 10th July 2012 | An Overview on Multitangents Functions, in Connection with the Multizeta Values, "" seminar in Paris XIII University (France). | ||
| 4th July 2012 | About links between multizeta values and multitangent functions, at the conference "Periods and Motives, A Modern Perspective on Renormalization", I.C.M.A.T., Madrid (Spain). |
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| 20th June 2012 | Variations around elliptic analogue of multizeta values and multitangent functions, working group C.A.R.M.A., Besse, (France). | ||
| 03th April 2012 | About Analytic Invariant of Tangent to Identity Diffeomorphisms, seminar in Strasbourg University (France). |
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| 29th March 2012 | About Analytic Invariant of Tangent to Identity Diffeomorphisms, seminar in Rennes 1 University (France). | ||
| 26th March 2012 | About Analytic Invariant of Tangent to Identity Diffeomorphisms, seminar in Lille 1 University (France). | ||
| 27th Febuary 2012 | Renormalization of Multitangent Functions and Applications, at the conference "Combinatorics of Mathematical Renormalization, a special day", I.H.E.S, Bures-sur-Yvette (France). |
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| 20th January 2012 | Multizêtas vs. multitangents, seminar in Clermond-Ferrand University (France). |
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| 15th November 2011 | On an Explicit Calculation of Horn Map : Links Between the Horn Map, Multitangent Functions and Multizeta Values, at the conference "Mould Calculus, Resurgence and Combinatorial Hopf Algebras", Scuola Normale Superiore di Pisa, Centro di Ricerca, Matematica, Ennio de Georgi, Pisa (Italia). |
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| 19th October 2011 | Analytic Invariant of Tangent to Identity Diffeomorphisms and Multizetas values, Ph.D. defense, Paris 11 University (France). |
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| 19th May 2010 | Introduction to Mould Calculus: About the Example of Poincaré's Linearisation Theorem, , Ph.D. students' seminar, Paris 11 University (France). |
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| 19th January 2009 | Efficient Process for Multiple Numerical Evaluations of Hyperlogarithms, Ph.D. students' seminar, Paris 11 University (France). |
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